Basis Point Calculator

What is a Basis Point (BPS)?

A basis point (often abbreviated as BPS, bp, or pronounced as "bip") is a common unit of measure for interest rates and other percentages in finance. One basis point is equal to 1/100th of 1%, or 0.01% (0.0001 in decimal form), and 0.1‰ in permille.

Basis points are typically used to express small changes in financial instruments, especially where differences of less than 1% are significant. Examples include interest rates, bond yields, credit spreads, and stock market indices. By using basis points, financial professionals avoid the ambiguity of discussing percentage changes of percentages.

Basis Point Formulas & Calculations

To convert between basis points and percentages or decimals, use the following simple formulas:

• Basis Points to Percentage: $\text{Percentage (\%)} = \frac{\text{BPS}}{100}$
• Percentage to Basis Points: $\text{BPS} = \text{Percentage (\%)} \times 100$
• Basis Points to Decimal: $\text{Decimal} = \frac{\text{BPS}}{10000}$
• Decimal to Basis Points: $\text{BPS} = \text{Decimal} \times 10000$

Calculating Basis Point Differences

When comparing two interest rates or yields, the difference in basis points is calculated as:

$$\text{BPS Difference} = (\text{Rate}_2 - \text{Rate}_1) \times 10000$$

For instance, if a bond yield increases from $4.25\%$ ($0.0425$) to $4.75\%$ ($0.0475$), the difference is:

$$(0.0475 - 0.0425) \times 10000 = 50 \text{ BPS}$$

Why Use Basis Points?

Using basis points eliminates confusion. For example, if an interest rate is $10\%$ and it experiences a "1% increase," does it mean the new rate is $11\%$ (absolute increase) or $10.1\%$ (relative increase)? By stating the rate increased by "100 basis points," it is clear that the new rate is $11\%$. If it increased by "10 basis points," the new rate is $10.1\%$.